Someone’s skin remedy is safe (6)
I believe the answer is:
secure
'is safe' is the definition.
('secure' can be a synonym of 'safe')
'someone's skin remedy' is the wordplay.
'skin' suggests removing the centre.
'remedy' becomes 'cure' ('cure' can be a synonym of 'remedy').
'someone' with its centre removed is 'se'.
'se'+'cure'='SECURE'
(Other definitions for secure that I've seen before include "Fixed or fastened so as not to give way" , "Safe; fixed" , "Free from danger or risk" , "Make safe or fasten" , "Firmly fixed or free from uncertainty" .)